James Gray's goal wasn't enough for Stanley to advance in the Capital One Cup as a brace from Souleymane Doukara put Leeds United through to Round Two.
The French striker plundered two goals in the first half, which was enough for the Championship hosts, despite a brave second-half comeback from the Reds.
James Beattie made two changes from the weekend loss to Southend as Jordan Mustoe and James Alabi made their full debuts for the club with Michael Liddle and Luke Joyce the players to miss out.
Luke Simpson continued in goal following his fine display on Saturday afternoon with new goalkeeper Jay Lynch having to settle for a place on the bench. He was joined by Will Hatfield, who hadn't fully recovered from injury to start against his former club.
Stanley enjoyed a positive start and had a few efforts on goal though the strikes from Piero Mingoia and Kal Naismith were never causing home goalkeeper Stuart Taylor too much trouble.
James Gray's tireless running almost earned a penalty as he was bundled over clumsily in the area but referee Richard Clark waved away the striker's protests.
The hosts came back into the game and took the lead after 20 minutes as Doukara collected a pass from the wing and spun away from Adam Buxton before arrowing a shot across Simpson and into the bottom corner.
Looking to respond to that setback immediately, Josh Windass danced between defenders and found space in the box but his shot lacked conviction and trickled harmlessly past the post.
Leeds then showed their class as they doubled their advantage shortly before the interval with Doukara again on the scoresheet. The striker burst past Dean Winnard and finished powerfully past Simpson.
There was a change in personnel - and formation - at the break as Rob Atkinson replaced Naismith with the Reds switching to 3-5-2. However, the second half started as the first ended - with Leeds on the attack but Matt Smith's volley flew over the bar from Charlie Taylor's left-wing cross.
Atkinson threatened to pull a goal back for Beattie's men as he met Mingoia's free-kick but the defender's header landed on top of the net.
The change in formation worked a treat for Accrington, who dominated the second half and Alabi went close, but could only shoot at Taylor after working some space in the box.
Hatfield came on to replace Nicky Hunt and had an immediate impact, setting up Gray to halve the deficit.
Tom Aldred set the midfielder away on the left and he pulled the ball back for Gray to smash home with the defender unable to stop the shot on the line.
After being the provider, Hatfield was almost the scorer but he could only flick a shot agonisingly wide of the post as Stanley stayed well in the ascendancy heading into the final stages of the game.
The Reds' cause was helped as Gaetano Berrardi saw red for a full-blooded lunge on Hatfield and the debutant received his marching orders.
However, Beattie's men could not find a leveller in the five minutes of stoppage time and ultimately fell at the first hurdle.
Stanley: Simpson; Buxton, Aldred, Winnard, Mustoe; Mingoia, Hunt (Hatfield 74), Windass, Naismith (Atkinson 45); Alabi, Gray.
Subs: Lynch, Liddle, Martin, McCartan, Bowerman.